Ground states for fractional Schrodinger equations involving critical or supercritical exponent

In this paper, we study the following fractional Schrodinger equation involving critical or supercritical exponent (-Delta)(s)u + V(x)u =lambda vertical bar u vertical bar(p-2)u + f (x, u), x is an element of R-N, where 0 < s < 1, N > 2s, 2(s)* = 2N/N-2s, p >= 2(s)*, lambda > 0, (-Delta)(s) denotes the fractional Laplacian of order s and f is a continuous superlinear but subcritical nonlinearity. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for small lambda > 0 by the Nehari method. Our main contribution is that we are able to deal with the supercritical case p > 2(s)*.